Pore network modeling of the effects of viscosity ratio and pressure gradient on steady-state incompressible two-phase flow in porous media

TL;DR

This study uses extensive pore network simulations to analyze how viscosity ratios and pressure gradients influence steady-state two-phase flow in porous media, revealing complex behaviors in relative permeability and flow mobilization.

Contribution

It provides new insights into the effects of viscosity ratio and pressure gradient on flow characteristics, challenging previous assumptions about relative permeability convergence at high capillary numbers.

Findings

Relative permeabilities and residual saturations show qualitative similarities to experimental studies.

Departure from straight-line relative permeability occurs with fluid mixing at different viscosity ratios.

Mobility ratios can vary non-monotonically with pressure gradient, especially with viscous fluids.

Abstract

We perform more than 6000 steady-state simulations with a dynamic pore network model, corresponding to a large span in viscosity ratios and capillary numbers. From these simulations, dimensionless quantities such as relative permeabilities, residual saturations, mobility ratios and fractional flows are computed. Relative permeabilities and residual saturations show many of the same qualitative features observed in other experimental and modeling studies. However, while other studies find that relative permeabilities converge to straight lines at high capillary numbers we find that this is not the case when viscosity ratios are different from 1. Our conclusion is that departure from straight lines occurs when fluids mix rather than form decoupled flow channels. Another consequence of the mixing is that computed fractional flow curves, plotted against saturation, lie closer to the diagonal than they would otherwise do. At lower capillary numbers, fractional flow curves have a classical S-shape. Ratios of average mobility to their high-capillary number limit values are also considered. These vary, roughly, between 0 and 1, although values larger than 1 are also observed. For a given saturation and viscosity ratio, the mobilities are not always monotonically increasing with the pressure gradient. While increasing the pressure gradient mobilizes more fluid and activates more flow paths, when the mobilized fluid is more viscous, a reduction in average mobility may occur.